Solve 1-x-1/2<x/4

$$1- \frac{ x-1 }{ 2 } < \frac{ x }{ 4 }$$

Solve for x

$$x>2$$

Solution Steps

Multiply both sides of the equation by 4, the least common multiple of 2,4. Since 4 is positive, the inequality direction remains the same.

$$4-2\left(x-1\right)<x$$

Use the distributive property to multiply -2 by x-1.

$$4-2x+2<x$$

Add 4 and 2 to get 6.

$$6-2x<x$$

Subtract x from both sides.

$$6-2x-x<0$$

Combine -2x and -x to get -3x.

$$6-3x<0$$

Subtract 6 from both sides. Anything subtracted from zero gives its negation.

$$-3x<-6$$

Divide both sides by -3. Since -3 is negative, the inequality direction is changed.

$$x>\frac{-6}{-3}$$

Divide -6 by -3 to get 2.

$$x>2$$